Geometric integration theory / by Hassler Whitney.

Format:

Book

Author/Creator:

Whitney, Hassler, author.

Series:

Princeton legacy library.

Princeton mathematical series ; 21.

Princeton Legacy Library

Princeton Mathematical Series ; 21

Language:

English

Subjects (All):

Integrals, Generalized.

Numerical integration.

Physical Description:

1 online resource (404 p.)

Place of Publication:

Princeton, New Jersey : Princeton University Press, 1957.

Language Note:

In English.

Summary:

A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems.Originally published in 1957.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Contents:

Frontmatter

Preface

Table of Contents

Introduction

A. The general problem of integration

B. Some classical topics

C. Indications of general theory

Part I: Classical theory

Chapter I. Grassmann algebra

Chapter II. Differential forms

Chapter III. Riemann integration theory

Chapter IV. Smooth manifolds

Part II: General theory

Chapter V. Abstract integration theory

Chapter VI. Some relations between chains and functions

Chapter VII. General properties of chains and cochains

Chapter VIII. Chains and cochains in open sets

Part III: Lebesgue theory

Chapter IX. Flat cochains and differential forms

Chapter X. Lipschitz mappings

Chapter XI. Chains and additive set functions

Appendix I. Vector and linear spaces

Appendix II. Geometric and topological preliminaries

Appendix III. Analytical preliminaries

Index of symbols

Index of terms

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

Description based on print version record.

Includes indexes.

ISBN:

9780691652900

0691652902

9781400877577

1400877571

OCLC:

957504768